Diffusion of activated ATM explains γH2AX and MDC1 spread beyond the DNA damage site

Summary During DNA repair, ATM-induced H2AX histone phosphorylation and MDC1 recruitment spread megabases beyond the damage site. While loop extrusion has been suggested to drive this spread, the underlying mechanism remains unclear. Herein, we provide two lines of evidence that loop extrusion is not the only driver of damage-induced γH2AX spread. First, cohesin loader NIPBL and cohesin subunit RAD21 accumulate considerably later than the phosphorylation of H2AX and MDC1 recruitment at micro-IR-induced damage. Second, auxin-induced RAD21 depletion does not affect γH2AX/MDC1 spread following micro-irradiation or DSB induction by zeocin. To determine if diffusion of activated ATM could account for the observed behavior, we measured the exchange rate and diffusion constants of ATM and MDC1 within damaged and unperturbed chromatin. Using these measurements, we introduced a quantitative model in which the freely diffusing activated ATM phosphorylates H2AX. This model faithfully describes the dynamics of ATM and subsequent γH2AX/MDC1 spread at complex DNA lesions.

(C) Comparison between the experimentally measured and predicted (Minimal model) spatial distribution of MDC1 concentration across the sites of complex DNA damage at s after micro-irradiation.
(D) Comparison between the experimentally measured and predicted (Confined model) spatial distribution of MDC1 concentration across the sites of complex DNA damage at s after micro-irradiation.

Figure S3
. Comparison between the experimentally measured and predicted spatial distribution of ATM concentration across the sites of complex DNA damage at 120 s after micro-irradiation, related to Figure 5.
(A) Microscopy images and simulation of ATM recruitment based on each model's best fit parameters.Grey images represent the images of ATM recruitment generated according to the model."A" refers to freely diffusing inactive ATM, "AX" refers to inactive ATM bound to the damage site, "P" refers to freely diffusing active ATM (αATM), and "PX" refers to active ATM bound to the damage site.Microscopy images are colored in green.Scale bar: 5 µm.(A) Microscopy images and simulation of ATM recruitment based on the Standard model's best fit parameters.Grey images represent the images of ATM recruitment generated according to the model."A" refers to freely diffusing inactive ATM, "AX" refers to inactive ATM bound to the damage site, "P" refers to freely diffusing active ATM, and "PX" refers to active ATM bound to the damage site.Microscopy images are colored in green.Scale bar: 5 µm.(C) Microscopy images and simulation of ATM recruitment based on the Minimal model's best fit parameters.Grey images represent the images of ATM recruitment generated according to the model."A" refers to freely diffusing inactive ATM, "AX" refers to inactive ATM bound to the damage site, "P" refers to freely diffusing active ATM (αATM), and "PX" refers to active ATM bound to the damage site.Microscopy images are colored in green.Scale bar: 5 µm.The damage site recruits free ATM protein, which binds to the damage site and is activated.The activated ATM then facilitates the phosphorilation of histones to which MDC1 binds.Here we consider 4 different reaction-diffusion models which could describe this system.
Throughout we make the following geometric assumption: The cell is cylindrical with radius R and the damage site, which we refer to as "focus", is in the middle.This geometry enables us to use symmetry and reduce dimensionality.
We will consider the interaction between the following species: the DNA damage (denoted by X, which are treated as parameters), the enzyme ATM (denoted by ATM) and the activated ATM (denoted by αATM), the histones (denoted by H2AX) and phosphirlated histones (denoted by γH2AX).The free MDC1 is denoted by S and the bound MDC1 is denoted by γH2AXMDC1 for the two foci.The spatial dependence is implicit everywhere.X has different initial values at the two foci, and is 0 everywhere else in the nucleus.The histones are present everywhere.The species which diffuse are the ATM and activated ATM and the free MDC1.The diffusion constants for ATM is D a , for activated ATM it is D p , and for free MDC1 is D m .
1.1.Standard model.Activation of ATM from ATM to αATM happens only in the damaged site and modifies the damage irreversibly.The damage has two forms, X and X 1 , where X leads to the complex ATMX and X 1 leads to the bound state B. The reactions can be reversible, and the ATM-damage complex can transition into three states.
activated ATM and modified damage site Following the dynamics of ATM, the activated ATM phosphorilates the histones H2AX to γH2AX.Once the histones are phosphorilated by the activated ATM, MDC1 then attaches to them.In the main model both αATM and αATMX phosphorilate the histone at the given location and act as enzymes.
For MDC1 we have the following equations Note that here we used the fact that and also that X 1 (0) = 0, B(0) = 0, to solve for ) and then substitute it in the equation . Some of the initial values can be determined from the data.Assuming that ATM's initial concentration (also number of molecules at the focus) is much bigger than the damage X and X 1 , at steady state each initial damage site would be bound to an ATM molecule, so B(t = ∞) = X 1 (t = 0) and ATMX(t = ∞) = X(t = 0).Also, ATM(t = 0) is the initial concentration of AT M , all of which is free inactive before the damage.
1.2.Minimal model: no αATMX.Here the intermediate compound αATMX is missing, i.e. there is no active αATM bound to the damage site: ATMX ATM forms a complex in the damaged site, Here thus only αATM phosphorilates the histones.The corresponding equations are as follows: and the MDC1 equations are 1.3.Confined model: no active αATM.Here ATM is only active when bound to the damage site and thus no αATM is formed.
ATMX ATM forms a complex in the damaged site,

of ATM remains bound to the focus
Here only αATMX phosphorilates the histones.The equations are: and MDC1 equations:

FRAP MODELS
In the FRAP experiment, the site is bleached at a given time T after the initial damage.Before that all particles are light.Particles in the bleached area become dark, and the dynamics continues.In order to model this we introduce light and dark species for each compound (each form of ATM), which we denote with subscripts ℓ and d respectively.
At the time of the photobleaching at the focus we have the following conditions.At time t = T all light species in a disc or radius r near the focus become dark, so the values of the light species become 0, the dark values are equal to the concentration of the corresponding light species at t = T − at the given spot.All other dark values are set to 0, and the light values remain the same.
Before the FRAP experiment the dynamics evolves according to the models from Section 1.We show this here with the Standard model, the other models are implemented completely analogously.
After photobleaching at time t = T we now have light and dark species, whose dynamics is governed as follows For the model with inhibitor we have the same dynamics for t < T .

ATM + X
After photobleaching the system at the presence of the inhibitor, we are assuming that X 1 has all been converted to B and the last reaction does not happen.
2.1.MDC1 FRAP experiment.Again, we run the original experiment with the equations above until a time t = T , when all MDC molecules are only light.We bleach a region of radius r around the focus at time t = T at which point all MDC (bound and free) in the focus becomes dark, and the reactions continue with two types of MDC -light and dark: Before the bleaching everything is light and we have the following reactions: For ||x − f ocus|| ≤ r: MDC1 ℓ (x) = 0, γH2AXMDC1 ℓ (x) = 0, MDC1 d (x) = MDC1(x), γH2AXMDC1 d (x) = γH2AXMDC1(x).
And the system of equations becomes: = ⃗ G i ( ⃗ F i (t)) then the two can put together as:

Figure S2 .
Figure S2.Comparison between the experimentally measured and predicted spatial distribution of MDC1 concentration across the sites of complex DNA damage at s after micro-irradiation, related to Figure 4. (A) Microscopy images and simulation of MDC1 recruitment based on each model's best fit parameters.Grey images represent the images of MDC1 recruitment generated according to the model.Microscopy images are colored in green.Scale bar: 5 µm.(B) Comparison between the experimentally measured and predicted (Standard model) spatial distribution of MDC1 concentration across the sites of complex DNA damage at s after micro-irradiation.
(B) Comparison between the experimentally measured and predicted (Standard model) spatial distribution of ATM concentration across the sites of complex DNA damage at 120 s after micro-irradiation.(C)Comparison between the experimentally measured and predicted (Minimal model) spatial distribution of ATM concentration across the sites of complex DNA damage at 120 s after micro-irradiation.(D)Comparison between the experimentally measured and predicted (Confined model) spatial distribution of ATM concentration across the sites of complex DNA damage at 120 s after micro-irradiation.

Figure S4 .
Figure S4.Comparison between the predicted spatial distribution of ATM and MDC1 concentrations across sites of complex DNA damage at 310 s after micro-irradiation, related to Figures 4 and 5. (A) Microscopy images and simulation of MDC1 recruitment based on each model's best fit parameters.Grey images represent the images of ATM recruitment generated according to the three models.Microscopy images are colored in green.Scale bar: 5 µm.(B) Comparison between predicted spatial distribution of ATM and MDC1 concentration across the sites of complex DNA damage at 310 s after micro-irradiation based on the Standard model.(C)Microscopy images and simulation of ATM recruitment based on each model's best fit parameters.Grey images represent the images of ATM recruitment generated according to the model."A" refers to freely diffusing inactive ATM, "AX" refers to inactive ATM bound to the damage site, "P" refers to freely diffusing active ATM (αATM), and "PX" refers to active ATM bound to the damage site.Microscopy images are colored in green.Scale bar: 5 µm.(D)Comparison between predicted spatial distribution of ATM and MDC1 concentration across the sites of complex DNA damage at 310 s after micro-irradiation based on the Minimal model.(E)Comparison between predicted spatial distribution of ATM and MDC1 concentration across the sites of complex DNA damage at 310 s after micro-irradiation based on the Confined model.

Figure S5 .
Figure S5.Modelling of protein dynamics at micro-irradiation-induced complex lesions after FRAP, related to Figure 7. (A) Comparison of ATM dynamics at complex lesions with (N = 16 foci) and without (N = 17 foci) FRAP.(B) Comparison of measured ATM dynamics at complex lesions after FRAP (N = 16 foci) with those predicted based on the standard model.

Figure S6 .
Figure S6.Comparison between the predicted spatial distribution of active/inactive and bound/freely diffusing ATM populations across the sites of complex DNA damage at 195 s after micro-irradiation, related to Figure 5.

(
B) Comparison between the predicted (Standard model) spatial distribution of AX, PX, and P at the DNA damage site at 195 s after micro-irradiation.The second graph in B is shown on a blown-up scale of the first graph.
(D) Comparison between the predicted (Minimal model) spatial distribution of AX, PX, and P at the DNA damage site at 195 s after micro-irradiation.The second graph in D is shown on a blown-up scale of the first graph.(E)Microscopy images and simulation of ATM recruitment based on the Confined model's best fit parameters.Grey images represent the images of ATM recruitment generated according to the model."A" refers to freely diffusing inactive ATM, "AX" refers to inactive ATM bound to the damage site, "P" refers to freely diffusing active ATM, and "PX" refers to active ATM bound to the damage site.Microscopy images are colored in green.Scale bar: 5 µm.(F)Comparison between the predicted (Confined model) spatial distribution of AX, PX, and P at the DNA damage site at 195 s after micro-irradiation.The second graph in F is shown on a blown-up scale of the first graph.
to phosphorilated histones This model translates to the following differential equations, where ∆ = ∇ 2 is the Laplace operator.All concentrations here are functions R 3+1 → R ≥0 .
f h * (αATM + αATMX) * H2AX + k r h * γH2AX d γH2AX dt = k f h * (αATM + αATMX) * H2AX − k r h * γH2AX +k of f (γH2AXMDC1 ℓ + γH2AXMDC1 d ) − k on γH2AX * (MDC1 ℓ + MDC1 d ) d γH2AXMDC1 ℓ dt = −k of f * γH2AXMDC1 ℓ + k on γH2AX * MDC1 ℓ d MDC1 ℓ dt = k of f * γH2AXMDC1 ℓ − k on γH2AX * MDC1 ℓ + D m ∆MDC1 ℓ d γH2AXMDC1 d dt = −k of f * γH2AXMDC1 d + k on γH2AX * MDC1 d d MDC1 d dt = k of f * γH2AXMDC1 d − k on γH2AX * MDC1 d + D m ∆MDC1 d 2.2.Timescale change.In order to implement and fit all models and experiments together with the same constants, we need to use the same timescale and δt.This is done as follows in general.Let the first model's experiment be on a time range from t = 0 to t = T 1 , and the second model run on time range from t = 0 to t = T 2 .Assuming we have equal number of time-point measurements (i.e. both arrays have equal lengths), we can run the models on the same time scale 0 to T 1 by multiplying the second model's equations by

Table S1
Rate constants, diffusion coefficients and concentrations of reactants of the reactions 1-19 that were measured during the experiments or obtained by fitting the mathematical models to experimental data, related to Figures4-7.